The Control of a Mathematical Analog of a Tentacle

A 2-dimensional dynamic analog of squid tentacles was presented. The tentacle analog consists of a multi-cell structure, which can be easily replicated to a large scale. Each cell of the model is a quadrilateral with unit masses at the corners. Each side of the quadrilateral is a spring-damper system in parallel. The spring constants are the controls for the system. The dynamics are subject to the constraint that the area of each quadrilateral must remain constant. The system dynamics was analyzed, and various equilibrium points were found with different controls. Then these equilibrium points were further determined experimentally, demonstrated to be asymptotically stable. A simulation built in MATLAB was used to find the convergence rates under different controls and damping coefficients. Finally, a control scheme was developed and used to drive the system to several configurations observed in real tentacle.

Balancing Belligerents or Feeding the Beast: Transforming Conflict Traps

Since the end of the Cold War, recurring civil conflicts have been the dominant form of violent armed conflict in the world, accounting for 70% of conflicts active between 2000-2013. Duration and intensity of episodes within recurring conflicts in Africa exhibit four behaviors characteristic of archetypal dynamic system structures. The overarching questions asked in this study are whether these patterns are robustly correlated with fundamental concepts of resiliency in dynamic systems that scale from micro-to macro levels; are they consistent with theoretical risk factors and causal mechanisms; and what are the policy implications. Econometric analysis and dynamic systems modeling of 36 conflicts in Africa between 1989 -2014 are combined with process tracing in a case study of Somalia to evaluate correlations between state characteristics, peace operations and foreign aid on the likelihood of observed conflict patterns, test hypothesized causal mechanisms across scales, and develop policy recommendations for increasing human security while decreasing resiliency of belligerents. Findings are that observed conflict patterns scale from micro to macro levels; are strongly correlated with state characteristics that proxy a mix of cooperative (e.g., gender equality) and coercive (e.g., security forces) conflict-balancing mechanisms; and are weakly correlated with UN and regional peace operations and humanitarian aid. Interactions between peace operations and aid interventions that effect conflict persistence at micro levels are not seen in macro level analysis, due to interdependent, micro-level feedback mechanisms, sequencing, and lagged effects. This study finds that the dynamic system structures associated with observed conflict patterns contain tipping points between balancing mechanisms at the interface of micro-macro level interactions that are determined as much by factors related to how intervention policies are designed and implemented, as what they are. Policy implications are that reducing risk of conflict persistence requires that peace operations and aid interventions (1) simultaneously increase transparency, promote inclusivity (with emphasis on gender equality), and empower local civilian involvement in accountability measures at the local levels; (2) build bridges to horizontally and vertically integrate across levels; and (3) pave pathways towards conflict transformation mechanisms and justice that scale from the individual, to community, regional, and national levels.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.